Kinetic immunoassay systems and methods

ABSTRACT

A microfluidic chip with an array of pillars for directing flow of beads is used to measure reaction kinetics. A stream may be continuously drawn from the reaction volume into the microfluidic chip. The bead is attached to a primary antibody. The reaction volume has an antigen and a second antibody with a label. The primary antibody binds to the antigen, and the secondary antibody binds to the antigen, creating a sandwich of bead, antigen, and label. The binding reactions occur over time in the reaction volume. The beads may be imaged after traversing a laminar wash buffer, and the signal intensity is measured. Each bead provides a kinetic monitoring of the immunoassay over the reaction time at which the bead is removed from the reaction media. Methods and systems are described in this disclosure.

BACKGROUND

Typical immunoassay technology carries out antibody binding reactionsreported by a label. The label measurement indicates the number of boundcomplexes after a combination of binding steps and wash procedures. Thewash procedures aim to remove excess label to avoid misrepresentation ofthe reaction label measurement.

FIG. 1 shows an example of a typical immunoassay. At stage 104,antibodies (e.g., antibody 108) are attached to a surface. Antigens(e.g., antigen 112) are in solution and may be captured by an antibody.The surface is washed to remove unbound antigens.

At stage 116, a labeling antibody (e.g., antibody 120 with label 124) isintroduced. Labeling antibodies bind to antigens that are bound toantibodies that are attached to the surface. The surface is washed againto remove unbound labeling antibodies.

At stage 128, a signal from the label is measured. A quantity of labelsis determined from the signal. A quantity of antigens is determined fromthe signal.

Immunoassay technologies currently available interrupt the bindingreaction to prepare the sample for label read out. The measurement isonly representative of the number of molecules having reacted up to thepoint when the reaction was interrupted. To repeat measurements for aspecific reaction time, the incubation time of the reaction and eachwash procedure should be identical, which requires a rigorous procedure.Calibration reactions may also need to be carried out simultaneously tobenchmark the label measurement.

Interrupting the binding reaction to fix the label intensity for readout results in an immunoassay measurement of a single point in time.Unless the reaction is incubated for several hours to reach reactionequilibrium, the point at which the reaction is interrupted takes placeduring a non-equilibrium binding kinetic phase of the reaction. Thesingle point measurement is impacted by the quality of the mixing,washing procedures, temperature, and other factors and can show greatvariability.

Embodiments described herein allow for real-time measurement of bindingreactions accurately and efficiently. Embodiments include these andother improvements.

BRIEF SUMMARY

A microfluidic chip with an array of pillars for directing flow of beadsis used to measure reaction kinetics. A nano/microliter stream may becontinuously drawn from the reaction volume into the microfluidic chip.The bead may be attached to a primary antibody. The reaction volume mayhave an antigen and a second antibody with a fluorescent label. Theprimary antibody may bind to the antigen, and the secondary antibody maybind to the antigen, creating a sandwich of bead, antigen, and label.The binding reactions occur over time in the reaction volume.

The beads are extracted from the reaction volume and sent across awashing buffer to remove non-specific interactions (unbound labels andantigens) from the bead surface. The beads may be imaged aftertraversing a laminar wash buffer, and the signal intensity is measured.The beads may be drawn from the binding reaction continuously over theduration of the reaction. When the beads arrive at the point of imagingand/or signal measurement, each bead has the same “time of flight” fromleaving the reaction media through wash, and imaging. This means thateach bead measurement represents the progress of the immunoassay at thetime of the specific bead leaving the reaction volume. Each beadprovides a kinetic monitoring of the immunoassay over the reaction timeat which the bead is removed from the reaction media.

In embodiments, methods may include mixing a first plurality of beadswith a sample to form a mixture in a reactor of a microfluidic chip. Thesample may include a plurality of analytes and a plurality of labels.Each bead of the first plurality of beads may be coupled to an affinityreagent. The affinity reagent may be configured to bind to the analyte.The plurality of labels may be configured to bind to the analyte.Methods may in addition include binding the plurality of analytes to aplurality of affinity agents coupled to the first plurality of beads inthe reactor. Methods may also include coupling a first subset of theplurality of labels to the first plurality of beads in the reactor.Methods may further include flowing a first portion of the mixture fromthe reactor through a first fluidic path defined by a plurality ofstructures in the microfluidic chip. The first portion of the mixturemay include the first plurality of beads coupled to the first subset ofthe plurality of labels. Methods may in addition include forming asecond mixture by flowing a solution in a second fluidic path. Thesecond fluidic path may intersect the first fluidic path. Methods mayalso include measuring an amount of the first subset of the plurality oflabels in the second mixture. Methods may further include determining areaction kinetic parameter using the amount of the first subset of theplurality of labels. Other embodiments may include correspondingcomputer systems, apparatus, and computer programs recorded on one ormore computer storage devices, each configured to perform the actions ofthe methods.

In embodiments, systems may include a microfluidic chip. Themicrofluidic chip may include a reactor. The microfluidic chip mayfurther include a plurality of structures defining a first fluidic path.The first fluidic path may be in fluid communication with the reactor, asolution reservoir, and a manifold configured to deliver a solution fromthe solution reservoir to intersect the first fluidic path. Systems mayin addition include a plurality of beads disposed on the microfluidicchip. Each bead of the plurality of beads may have a diameter smallerthan a width of the first fluidic path. Each bead of the plurality ofbeads may be bound to a first affinity reagent. Systems may also includean imaging detector. Other embodiments of this aspect includecorresponding computer systems, apparatus, and computer programsrecorded on one or more computer storage devices, each configured toperform the actions of the methods.

A system of one or more computers can be configured to performparticular operations or actions by virtue of having software, firmware,hardware, or a combination of them installed on the system that inoperation causes or cause the system to perform the actions. One or morecomputer programs can be configured to perform particular operations oractions by virtue of including instructions that, when executed by dataprocessing apparatus, cause the apparatus to perform the actions.

A better understanding of the nature and advantages of embodiments ofthe present invention may be gained with reference to the followingdetailed description and the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows an example of an immunoassay.

FIG. 2 shows a graph of a kinetic profile of a binding reaction.

FIG. 3A shows an example kinetic reaction profile for a binding reactionaccording to embodiments of the present invention.

FIG. 3B shows a rate function established by the affinity constants ofeach binding entity according to embodiments of the present invention.

FIG. 4 shows a reactor and the mechanisms allowing for accuratedetermination of kinetic parameters according to embodiments of thepresent invention.

FIG. 5A illustrates a microfluidic chip for analyzing reaction kineticparameters according to embodiments of the present invention.

FIG. 5B illustrates the mechanics of the washing of the beads accordingto embodiments of the present invention.

FIG. 6 depicts the relationship between sheer factor and displacementaccording to embodiments of the present invention.

FIGS. 7A, 7B, and 7C show possible orientations of structures accordingto embodiments of the present invention.

FIG. 8 shows a graph of reaction kinetic profiles generated with a DLDarray according to embodiments of the present invention.

FIG. 9A shows an example of multiplexing using different size beadsaccording to embodiments of the present invention.

FIG. 9B shows the distribution of beads at different locations in themicrofluidic chip according to embodiments of the present invention.

FIG. 10 is a graph of the bead intensity according to embodiments of thepresent invention.

FIG. 11 shows a graph of signal intensities over time according toembodiments of the present invention.

FIG. 12 shows a graph of reaction profiles with different ligandconcentrations according to embodiments of the present invention.

FIG. 13 is a flowchart of an example process for determining reactionkinetic parameters according to embodiments of the present invention.

FIG. 14 shows a system for analyzing reaction kinetics according toembodiments of the present invention.

FIG. 15 shows a computer system according to embodiments of the presentinvention.

DETAILED DESCRIPTION

Current techniques of measuring kinetics of reactions (e.g., binding ofan antigen to an affinity reagent) may involve interrupting a reactionto measure an amount at a specific time. Interrupting a reactionprevents real-time measurement of kinetics. Additionally, in order toobtain accurate and precise measurements, procedures may need to befollowed rigorously. Errors from slight variations in procedure willresult in inaccurate results, especially for fast reaction kinetics ormeasuring low concentrations of a reactant (e.g., an antigen).

Embodiments described herein include real-time measuring of the kineticsof reactions. Antigens, labels, affinity reagents, and beads may bemixed together in a batch reactor of a microfluidic chip. This time maybe time to, the start of the reaction. A reaction may take place thatmay result in a bead being bound to a first affinity reagent, which isbound to an antigen, which is then bound to a second affinity reagent,which is bound to a label. A bead be attached to several first affinityreagents. Beads may be flowed out of the reactor continuously at adiagonal. A first bead may leave the reactor at time t₁. A second beadmay leave the reactor at time t₂. A clean laminar flow may wash beads ina direction that intersects the diagonal. This flow may remove unboundlabels, antigens, and/or affinity reagents from the beads. This cleanlaminar flow also may quench any reaction. The beads that remain in thediagonal flow may be bound to affinity reagents, antigens, and labels.The amount of labels of the beads may be measured in real-time at anoutput location. For example, the label may be a fluorescent label, andthe intensity of the fluorescent signal may be measured.

The time of the signal measurement may be adjusted by the time the beadstake to reach the output location from the batch reactor. Amounts ofbound antigen can then be plotted versus time. Concentrations (e.g.,absolute or relative concentrations) and/or kinetic rate constants canbe determined using the measured amount of labels and the times of themeasurement.

Embodiments described herein may allow for an accurate assessment of thereaction kinetic through mathematically fitting of the antigenconcentration over time. The confidence in the concentration fitting maybe continuously calculated with each new bead being measured. Themeasurement may be ended, when the satisfactory confidence level isachieved from the real-time mathematical fitting.

Several thousand microbeads may be incubated in the immunoassayreaction. Less than 1,000 may be needed to achieve a high confidencekinetic profile of the reaction and yield a high accuracy measurement.The mathematical modeling of the reaction kinetic profile may achieve ahigh confidence concentration fitting after less than 5 minutes reactionfor antigens in the nanomolar range, and less than 10 minutes in thepicomolar range. Kinetics of binding reactions, dissociation reactions,and other reactions may be determined.

Systems and methods are described in further detail in this disclosure.

I. Reaction Kinetics

FIG. 2 shows a graph of a kinetic reaction profile of a binding reactionwith a given rate constant. The x-axis shows time. The y-axis showssignal intensity of a label indicating the completion of a bindingreaction. The to at the bottom indicates the initial time. The t_(eq)indicates the time at which the binding reaction is at equilibrium. Thedifferent lines correspond to different initial concentrations of areactant, with a higher line being a higher initial concentration. Theinitial phase of the binding reaction has a high slope. Monitoring theinitial phase rather than the equilibrium phase may allow for precisekinetic fitting and a quicker result.

FIG. 3A shows an example kinetic reaction profile for a bindingreaction. The x-axis shows the time in seconds. The y-axis shows thesignal intensity of a label in arbitrary units. Line L1 is the profilefor a first ligand (e.g., analyte, antigen) concentration. Line L2 isthe profile for a second ligand concentration. In endpoint detectiontechniques, measurements may be delayed until the reaction reachesequilibrium (e.g., at time t_(eq)) to determine the concentration. Asshown in FIG. 3A, the time may be around 10 minutes to reachequilibrium. Otherwise, measurements in the steep incline portion of theprofiles should be rigorously carried out in order to be repeatable andcomparable with other measurements.

FIG. 3B shows a rate function established by the affinity constants ofeach binding entity (i.e., affinity reagent). The equation includes thefollowing variables: I is the signal intensity; μS is the microbeadconcentration; A is the concentration of capture antibody (i.e., theconcentration of the beads multiplied by the number of binding sites perbead); L is the concentration of the ligand from the sample that isbeing measured; K_(D) is the dissociation constant of the complex;k_(on) is the on rate constant of the complex; and t is the time of thereaction.

A transfer function converts a signal intensity value to aligand/antigen concentration in the sample. With data of signalintensity as a function of time, the transfer function can use the ratefunction to determine the respective concentrations of each bindingentity to the number of complexes being formed. However, when thereaction is interrupted at a set incubation time as with endpointdetection, the value of the ligand concentration is inferred from acalibration curve. The calibration curve would need to be determinedfrom calibration samples and not from the test sample, and thecalibration samples would need to be measured in the same manner as thetest sample. Hence, using the rate function has advantages over endpointdetection in not needing a calibration performed.

With the kinetic reaction profile, the total ligand concentration can becalculated from fitting of the first few seconds of the reaction. Bycontrast, endpoint detection is typically performed at equilibrium,which may be minutes into the reaction.

Rate functions, such as in FIG. 3B, show that the ligand concentrationcan be calculated when the rate constants are known. Additionally, rateconstants may be calculated when ligand concentrations are known. Bothrate constants and ligand concentrations can be calculated from multipleexperiments to generate multiple kinetic reaction profile curves.

II. Kinetic Immunoassay Technique

Calculating kinetic parameters using rate functions can be performed inthe first few seconds of the reaction if the signals for a boundreaction for a given reaction time can be determined accurately.

FIG. 4 illustrates the reactor and the mechanisms allowing for accuratedetermination of kinetic parameters. Reactor 404 contains capture beads,including capture bead 408. Capture beads may be bound to captureantibodies, including antibody 410. Capture beads may bind with anantigen, including antigen 412. Antigens may bind with a labeledsandwich antibody, including labelled sandwich antibody 416. The labeledsandwich antibody 416 includes label 420. Label 420 may be a quantumdot, fluorophore, chemiluminescent tag, electrochemical label, or othersuitable label. The expected binding reaction is a sandwich reaction424, which forms a complex of the capture beads bound to an antigenbound to a labeled sandwich antibody. The contents in the reactor may beincubated.

Arrow 428 represents a flow of material out of reactor 404. Area 432shows possible materials in the output of the reactor. The materialsillustrated include the product of a sandwich reaction, as well as anunbound antigen and an unbound labeled sandwich antibody. The beads maybe drawn out from reactor 404 at a constant rate over a fixed amount oftime.

Wash 436 represents a flow that removes the unbound antigen and unboundlabeled sandwich antibody from the product of the sandwich reaction. Thecapture beads are not removed by the wash and instead proceed in adirection indicated by arrow 440 and arrow 444, which are different fromthe direction of the wash. The wash direction may be from top to bottomin this figure rather than from left to right.

Bead 448 represents a capture bead that has had time t₁ in the reactor.Bead 452 represent a capture bead that has had time t₂ in the reactor,where t₂ is a longer time than t₁. Bead 448 is farther from reactor 404than bead 452 because bead 448 left reactor 404 at an earlier time thanbead 452. The same flow carries bead 448 and bead 452 so that bead 452cannot pass bead 448. Bead 452 is depicted as a bead that has capturedmore than one antigen, each coupled to a labeled sandwich antibody. Bead452 has spent longer in reactor 404 than bead 448 so bead 452 maycapture more antigens.

The signal from the label or labels may be detected and quantified. Theintensity of the signal may be related (e.g., proportional) to theamount of antigen on a bead. The signal intensity may be analyzed orplotted over time. A kinetic reaction profile can be determined from thesignal intensity.

The error on each bead measurement may be controlled by the ensemble ofmolecules bound to the bead. The number of binding sites on each bead isknown, and the number of ligands that should be bound to each bead maybe mathematically known for any given time value. The error may bemathematically calibrated. For determinations of whether a concentrationis above a threshold, a 99% confidence level may be achieved rapidly(e.g., within 5 minutes in the picomolar range). For example, a kineticreaction profile may be used to determine whether the concentration oftroponin I is above a threshold concentration that indicates a heartattack.

FIG. 5A illustrates a microfluidic chip for analyzing reaction kineticparameters. One or more channels (e.g., channel 504) may lead to imaginginput area 508. The channels may be from a reactor (e.g., reactor 404 inFIG. 4 ) or from a reservoir for a wash solution. Imaging input area 508allows for brightfield images of beads with labels and unbound labels tobe taken. Imaging input area 508 is optional. FIG. 5A is not shown toscale.

After going through imaging input area 508, the bead mixture goesthrough deterministic lateral displacement (DLD) array 512. DLD arraysare described in U.S. Pat. No. 7,150,812, the entire contents of whichare incorporated herein by reference for all purposes. DLD array 512 mayinclude a plurality of structures. The structures may be pillars with acircular base or a rectangular (e.g., square) base. The structures maybe in a regularly spaced array. The array may define straight pathsthrough the structures. These straight paths may be offset from the pathgoing from the channels through the imaging input area. The straightpaths through DLD array 512 may not be parallel to the longitudinal axisof the chip. In FIG. 5A, the longitudinal axis is illustrated in thevertical direction. FIG. 5A shows fewer structures than would betypically present in a DLD array for the sake of clarity ofillustration.

The dashed lines indicate paths (e.g., path 516) that the beads followthrough the DLD array. These paths are at a diagonal from imaging inputarea 508. The beads travel and are displaced laterally from their input.The beads travel to imaging output area 520. Imaging output area 520 islaterally displaced from imaging input area 508.

The solid lines indicate paths (e.g., path 524) that a cleaning flow mayfollow. This cleaning flow may be delivered from one or more channels.The cleaning flow may be along the longitudinal axis. The cleaning flowdirects unbound antigens and antibodies away from the beads, effectivelywashing the beads. With the longitudinal direction of the cleaning flow,the cleaning flow may go to imaging output area 528, which is alignedwith imaging input area 508. Although only a few solid lines areillustrated, the cleaning flow may cover most (50%, 60%, 70%, 80%, 90%or more) or the entirety of the DLD array, washing beads throughouttheir travel to imaging output area 520. Imaging output area 520 is forbrightfield imaging and is optional.

At measurement area 536, the labels may be measured. Measurement area536 may be a section of the structures. The beads follow consistent andpredictable paths between structures, and signals from the labels of thebeads can be reliably measured by an imaging device or other detector.For example, a high sensitivity quantitative CMOS camera may imagemicrobeads and detect down to a single fluorescent or photoluminescentlabel. The cleaning flow may remove other labels to decrease oreliminate background signal. The cleaning flow may fully replace theliquid volume around each bead up to several hundred times.

The output from imaging output area 520 and imaging output area 528 is adebris filtering section 532. Beads, antigens, and antibodies exit themicrofluidic chip in this area. Debris filtering section 532 isoptional.

The total immunoassay reaction may be as small as 10 microliters. Thesampling of the reaction may be carried out on less than 5 microliters.

FIG. 5B illustrates the mechanics of the washing of the beads. Bead 550has non-specific interactions with labeled sandwich antibody 554 andother labeled sandwich antibodies. In this example, bead 550 is notbound to any antibodies and therefore is not bound to any antigens,which are therefore not bound to any labeled sandwich antibodies.

Arrows, including arrow 558, show laminar flow of a buffer solution.This flow cleans bead 550 of non-specific interactions. The flow of thebuffer solution may be similar to path 524 in FIG. 5A. The flow may bein a direction parallel to the longitudinal axis of the microfluidicchip. The unbound labeled sandwich antibodies (e.g., labeled sandwichantibody 562) are washed away from bead 550 in the direction of the flowof the buffer solution.

Bead 550 is laterally displaced, which may be as explained with DLDarray 512 in FIG. 5A. After lateral displacement, bead 566 may be cleanwith little or no labeled sandwich antibodies nearby (e.g., within adistance equal to the diameter of the bead).

FIG. 6 depicts the relationship between sheer factor and displacement. Alaminar flow is in they direction (vertical) in the figure. Bead 604 isdisplaced in both they direction and x direction (horizontal) intraveling diagonally. Bead 604 is subjected to a Sheer factor, which isthe force applied by the laminar flow on non-specifically boundentities. The Sheer factor is the difference between the vertical (y)velocity of bead 604 and the laminar flow. The x displacement determineshow many times the liquid volume around the bead is fully renewed. Inembodiments, a 6 μm bead that travels 5 mm in the x direction results inthe buffer around the bead (i.e., any liquid in contact with the beadsurface) being exchanged 833 times.

FIGS. 7A-7C illustrate possible orientations of structures. Thestructures are offset from the longitudinal axis of the microfluidicchip to create lateral displacement in the flow of the beads. FIG. 7Ashows the largest offset angle, and FIG. 7C shows the smallest offsetangle. FIG. 7A shows an orientation of structures where starting from agiven structure, three additional structures are passed to reach astructure that is shifted one over to the left from the startingstructure. The shift is denoted as λ, which is the distance from thecenter of one structure to the center of the adjacent structure. Theangle of the offset can be calculated from tan⁻¹ (1/3). The orientationis denoted as N=3, where 3 is the number of structures for a shift tothe right. FIG. 7B shows an orientation of N=5. FIG. 7C shows anorientation of N=10.

A lower N value will result in larger diameter beads being shiftedlaterally but may not move smaller diameter beads laterally. Therelationship between the critical diameter and the N value can bedetermined from an empirical equation:

$\begin{matrix}{\frac{D_{C}}{G} \cong {\alpha \times \epsilon^{\beta}}} \\{\epsilon = \frac{1}{N}}\end{matrix}$where Dc is the critical diameter of the beads, G is the gap distancebetween adjacent structures, N is the value described in FIGS. 7A-7C,and α and β are fitted parameters.

The gap spacing, G, may be equal to or about equal to the height of thestructures. The gap spacing, G, may also be equal to or about equal tothe diameter of the structures. The diameter of the structure may be aneffective diameter of the structure if the structure does not have acircular cross section. The effective diameter can be the diameter for acircle having the same area as the cross section of the structure. As anexample, the gap spacing, height, and diameter of the structures may allequal to 20 μm.

III. Estimating Reaction Kinetic Parameters

Systems and methods described herein can be used to analyze kinetics ofdifferent reactions.

A. Dissociation Rate Constants

The dissociation rate constant (k_(off)) was estimated with methods andsystems described herein. In this experiment, the sandwich immunoassaywas performed with human C reactive protein (hCRP). The immunoassay wasincubated until equilibrium, and then the beads were run through the DLDarray. The washed beads were trapped in holding traps designed in thechip, and the signal decay was monitored over time on a few beads todetect the signal loss function.

FIG. 8 shows a graph of reaction kinetic profiles generated with a DLDarray and methods described herein. The x-axis shows time in minutes.The y-axis shows the signal intensity in arbitrary units. Each linecorresponds to signal decay of a single microbead. All microbeads arefrom the same reaction, so are expected to have a similar k_(off).

The intensity of labels as a function of time can be represented by:I(t)=I₀e^(-k) ^(off) ^(xt)where I₀ is the initial intensity of the labels bound to microspheres,k_(off) is the dissociation rate constant, and t is time.

The intensities at different times can be fit to the equation andk_(off) can be determined. The determined k_(off) are shown in FIG. 8 .The fit shows that we have a single exponential fit, and thisdemonstrates that only sandwich bound signal is being detected, and therate at which it decays corresponds to the known k_(off) value for thisantibody system. The R² values are provided, showing good fits to thedata.

B. Multiplexing

Different size beads and/or different types of labels can be used totest examine kinetics of different reactions with the same assay.

FIG. 9A shows an example with different size beads. Bead 904 is a 10 μmdiameter bead, bound to an antibody that captures C-reactive protein.Bead 908 is an 8.2 μm diameter bead, bound to an antibody that capturesIGF1. Bead 912 is a 5.8 μm diameter bead, bound to an antibody thatcaptures hepcidin. These beads, along with C-reactive protein, IGF1,hepcidin, and labeled sandwich antibodies are incubated in reactor 916.

Flow with beads is drawn from reactor 916 through a series of DLDarrays. Buffer from buffer reservoir 920 is flowed to wash the beads toremove non-specific interactions as described herein. The series of DLDarrays separates the different size beads laterally. The DLD arrays aredenoted as N_(m), where m denotes the number of rows of additionalpillars corresponding to a one-column shift in beads (indicated by N inFIGS. 7A-7C). The smallest beads (e.g., bead 912) follows path 924. Themedium beads (e.g., bead 908) follows path 928. The largest beads (e.g.,bead 904) follows path 932.

FIG. 9B shows the distribution of beads at different locations in themicrofluidic chip. The smallest beads, bead 912, are displaced the leastamount laterally, ending in port 3 and target channels 13-19 (indicatedby box 936). Bead 908 is displaced an intermediate amount laterally,ending mostly in port 5 and target channels 23-31 (indicated by box940). The largest beads, bead 904, is displaced the largest amountlaterally, ending mostly in port 7 and target channels 35-43 (indicatedby box 944).

The results show that different size beads can be used to analyze thekinetics or concentrations of different antigens at the same time.

C. Signal Intensity Versus Time

The signal intensity was tracked over time using methods and systemsdescribed herein. The beads are attached to streptavidin. Biotin islabeled with quantum dots. Streptavidin has a high affinity to bind withbiotin.

Images of beads having reaction times of 1 min., 8 min., and 23 min.show brighter (i.e., higher signal intensity) beads with longer reactiontimes.

FIG. 10 is a graph of the bead intensity. The x-axis is the x-coordinate(e.g., left to right in FIG. 5A) of the pixel. The x-axis spans 450pixels. The y-axis is the sum of the signal intensities from all pixelsat a given x-coordinate. FIG. 10 shows that higher reaction times leadto higher signal intensities from the beads.

FIG. 11 shows a graph of signal intensities over time for 10 μm beadsmodified with streptavidin and biotin labeled with quantum dots. Thex-axis is time in minutes. The y-axis is microsphere quantum dotoccupancy, which represents the number of dots on the surface of thebead and is a signal intensity. The reaction is run three times togenerate the data points in the graph. The fitted line is forillustrative purposes. The graph shows a kinetic reaction profile. Theprofile has a steep increase then levels off as the reaction approachesequilibrium.

D. Kinetic Measurements

An experiment verified the capability of methods and systems describedherein to analyze reaction kinetics in the picomolar concentrationrange.

FIG. 12 shows a graph of reaction profiles with different ligandconcentrations in the picomolar range. The x-axis is time in minutes.The y-axis is microbead occupancy. The three lines are fitted lines fordifferent concentrations of ligands: 1 pM, 3 pM, and 5 pM. The 5 pMligand has the steepest increase and the highest occupancy nearequilibrium. The 1 pM ligand has the least steep increase and the lowestoccupancy near equilibrium.

Data in this graph can be analyzed to determine rate constants for thereaction. Additionally, data can be used for calibration for additionalexperiments. The concentration of a sample can be determined based onhow closely the kinetic profile matches previous reaction data.

IV. Example Methods

FIG. 13 is a flowchart of an example process 1400. In someimplementations, one or more process blocks of FIG. 13 may be performedby a system, including system 1500 or any system described herein.

At block 1410, a first plurality of beads is mixed with a sample to forma mixture in a reactor of a microfluidic chip. The beads may includepolystyrene, iron-oxide, silica, polymer, metal (e.g., gold, silver), orany other suitable material. The sample may include a plurality ofanalytes and a plurality of label compounds. Each bead of the firstplurality of beads may be coupled to an affinity reagent. The analytemay be any analyte or ligand described herein. The affinity reagent maybe configured to bind to the analyte. Each bead may be coupled to aplurality of affinity reagents. The plurality of label compounds may beconfigured to bind to the analyte. The label compounds may be a labeledsandwich antibody, as described herein, which may include a detectablelabel and an antibody configured to bind the analyte. The plurality ofbeads may be spherical.

The sample may be prepared using a biological sample obtained from asubject. The biological sample may include blood, plasma, serum, urine,tissue, sweat, nasal excretions, or material from a mouth swab. In someembodiments, the biological sample may be from a subject that has atumor. The sample may be prepared by extracting or concentratinganalytes from the biological sample. In some embodiments, the sample mayexclude extracting or concentrating analytes.

The analyte may be an antigen. The antigen may be associated with adisease or a disorder. The antigen may be a protein. The antigen mayhave a concentration from 0 to 10 pM, 10 to 50 pM, 50 to 100 pM, 100 to500 pM, 500 pM to 1 μM, 1 to 10 μM, 10 to 50 μM, 50 to 100 μM, or 100 to500 μM. The antigen may be troponin I, C-reactive protein, IGF1,hepcidin, or any antigen described herein.

In some embodiments, the analyte may be a nucleic acid molecule. Forexample, the nucleic acid molecule may be DNA or RNA (e.g., mRNA). Thenucleic acid molecule may be a biomarker for a disorder or disease. Thenucleic acid molecule may be single-stranded.

The affinity reagent may be an antibody. The antibody may have anaffinity to bind with a protein that is the antigen.

In some embodiments, the affinity reagent may be an oligonucleotide. Theoligonucleotide may include a sequence of nucleotides complementary to aportion or all of the nucleic acid molecule analyte. The portion may beat least 3, 4, 5, 6, 7, 8, 9, 10, 10 to 15, 15 to 20, or 20 to 30nucleotides. In some embodiments, the entire sequence of the nucleicacid molecule is complementary to a subsequence of nucleotides in theoligonucleotide.

Each label of the plurality of label compounds may be a fluorescentlabel, a quantum dot, a chemiluminescent label, or an electrochemicallabel.

In some embodiments, the label compound may include an oligonucleotidethat includes a sequence of nucleotides complementary to a subsequenceof the nucleic acid molecule analyte. For example, a first part of thenucleic acid molecule analyte may hybridize with the oligonucleotideattached to the bead, and a second part of the nucleic acid moleculeanalyte may hybridize with the oligonucleotide of the label compound.

In some embodiments, the label compound may include an enzyme. Theenzyme may target double-stranded nucleic acid molecules. In thismanner, the enzyme may recognize a nucleic acid molecule that hashybridized with an oligonucleotide attached to a bead.

At block 1420, the plurality of analytes is bound to a plurality ofaffinity agents coupled to the first plurality of beads in the reactor.Other analytes may be unbound in the reactor at that point in time. Atlater times, other analytes may bind to other affinity reagents of otherbeads in the reactor.

At block 1430, a first subset of the plurality of label compounds iscoupled to the first plurality of beads in the reactor. Coupling thefirst plurality of the plurality of label compounds to the firstplurality of beads may occur before or after binding the plurality ofanalytes to the plurality of affinity reagents. For example, theplurality of label compounds may bind to the analytes before theanalytes are bound to the plurality of affinity reagents.

At block 1440, a first portion of the mixture is flowed from the reactorthrough a first fluidic path defined by a plurality of structures in themicrofluidic chip. The first portion of the mixture may include thefirst plurality of beads coupled to the first subset of the plurality oflabel compounds.

The plurality of structures may include a plurality of pillars. Theplurality of pillars may be a portion of an array of pillars. The arrayof pillars may be a DLD array, including any described herein. The arrayof pillars may be characterized by a plurality of rows and a pluralityof columns. The plurality of pillars may include pillars from at leastfive columns from the plurality of columns. In some embodiments, theplurality of pillars may include from 1 to 5 columns, from 5 to 10columns, from 10 to 20 columns, from 20 to 30 columns, from 30 to 50columns, or more than 50 columns from the plurality of columns. Thestructures in the plurality of structures may be identical.

The microfluidic chip may have a longitudinal axis. The first fluidicpath and the longitudinal axis may form an angle in a range from 10degrees to 60 degrees. For example, the angle may be in a range from 10to 20 degrees, from 20 to 30 degrees, from 30 to 40 degrees, from 40 to50 degrees, or from 50 to 60 degrees. The first fluidic path may be in adiagonal direction relative to the microfluidic chip. The first fluidicpath may be determined by the average (e.g., mean, median, or mode)direction of the first plurality of beads. The angle formed may be anangle calculated with FIGS. 7A to 7C. For example, the angle may beequal to or within 5% or 10% of tan⁻¹ (1/N), where N is an integer from1 to 30.

At block 1450, a second mixture is formed by flowing a solution in asecond fluidic path. The second fluidic path may intersect the firstfluidic path. The first fluidic path and the second fluidic path mayintersect at an angle in a range from 10 to 20 degrees, from 20 to 30degrees, from 30 to 40 degrees, from 40 to 50 degrees, or from 50 to 60degrees. The second fluidic path may be parallel to the longitudinalaxis. The second fluidic path may be determined by the average (e.g.,mean, median, or mode) direction of the solution. The initial directionof the second fluidic path may be in the same initial direction as theinitial flow from the reactor to the plurality of structures. Thesolution may include phosphate buffer saline (PBS).

Process 1400 may further include removing, using the solution, a secondsubset of the plurality of label compounds from the first portion of themixture to form a second mixture including the first plurality of beads.The second subset of the plurality of label compounds may not be coupledto the first plurality of beads. The solution may wash or clean thebeads of non-specific interactions as described herein.

Process 1400 may include removing unbound analytes. The plurality ofanalytes may be a first plurality of analytes. The method may furtherinclude removing, using the solution, a second plurality of analytes,where the second plurality of analytes is not coupled to the firstplurality of beads.

At block 1460, an amount of the first subset of the plurality of labelcompounds in the second mixture may be measured. Measuring the amount oflabel compounds may include measuring an intensity (e.g., a fluorescenceintensity, pixel intensity, or electrical current). The intensity may bea normalized intensity. The location for measurement may be at a firstdistance from a longitudinal axis going through the outlet of thereactor. The first distance may be in a range from 0 to 1 mm, 1 to 2 mm,2 to 3 mm, 3 to 4 mm, 4 to 5 mm, 5 to 10 mm, or greater than 10 mm. Thelocation for measurement may be at a second distance from the reactor.The second distance may be from 1 to 2 mm, 2 to 3 mm, 3 to 4 mm, 4 to 5mm, 5 to 10 mm, 10 to 15 mm, 15 to 20 mm, 20 to 30 mm, 30 to 50 mm, orgreater than 50 mm.

At block 1470, a reaction kinetic parameter is determined using theamount of the first subset of the plurality of label compounds. Thereaction kinetic parameter may be any parameter used in a kinetic rateequation. The reaction kinetic parameter may be a concentration of theplurality of analytes. For example, the concentration may be an absoluteor relative concentration in the reactor or in the sample. A relativeconcentration may be relative to the concentration of another analyte inthe reactor or in the sample. The reaction kinetic parameter may be arate constant characterizing a binding reaction of the affinity reagentto the analyte. The reaction kinetic parameter may be a rate constantcharacterizing a dissociation reaction of the affinity reagent to theanalyte. In some embodiments, the rate constants may be predetermined,and the concentration may be calculated using the predetermined rateconstant.

In some embodiments, the reaction kinetic parameter may be theconcentration of the plurality of analytes. The concentration may becompared to a threshold value. The threshold value may be a value of aconcentration that indicates the presence of a disorder, or thethreshold value may be a value of a concentration that is statisticallydifferent from the minimum concentration that indicates the presence ofa disorder. For example, the threshold value may be 1, 2, or 3 standarddeviations above the minimum concentration. When the analyte is troponinI, the threshold value may indicate the existence or onset of a heartattack.

Process 1400 may be multiplexed to analyze different analytes. Theplurality of analytes may be a plurality of first analytes. The samplemay include a plurality of second analytes. The first analyte may bedifferent from the second analyte. The plurality of affinity reagentsmay be a plurality of first affinity reagents. Process 1400 may furtherinclude mixing a second plurality of beads with the sample to form themixture. Each bead of the second plurality of beads may be coupled to asecond affinity reagent. The second affinity reagent may be configuredto bind to the second analyte. Process 1400 may include binding theplurality of second analytes to a plurality of second affinity reagentscoupled to the second plurality of beads.

The first plurality of beads may be characterized by diameters in afirst size range. The second plurality of beads may be characterized bydiameters in a second size range. The first size range may not be thesecond size range. Beads in additional size ranges may be used. Forexample, beads having 3, 4, 5, 6, 7, 8, 9, or 10 size ranges may beused. Beads may be in a range from 1 to 2 μm, 2 to 3 μm, 3 to 4 μm, 4 to5 μm, 5 to 6 μm, 6 to 7 μm, 7 to 8 μm, 8 to 9 μm, 9 to 10 μm, 10 to 11μm, 11 to 15 μm, 15 to 20 μm, 20 to 30 μm, or greater than 30 μm.

The plurality of structures may be a first plurality of structures.Process 1400 may further include flowing a second portion of the mixturefrom the reactor through a third fluidic path defined by a secondplurality of structures in the microfluidic chip. The second pluralityof structures may include different structures than the first pluralityof structures.

Process 1400 further includes coupling a third subset of the pluralityof label compounds to the second plurality of beads in the reactor.Process 1400 may include removing, using the solution, a fourth subsetof the plurality of label compounds from the second portion of themixture to form a fourth mixture including the second plurality ofbeads. Process 1400 may include measuring an amount of the third subsetof the plurality of label compounds in the fourth mixture.

The label compounds used may be different to analyze different types ofanalytes. The plurality of label compounds may be a plurality of firstlabel compounds. The sample may further include a plurality of secondlabel compounds. The plurality of second label compounds may beconfigured to bind to the second analyte. The plurality of second labelcompounds may be different from the plurality of first label compounds.Process 1400 may further include coupling a first subset of theplurality of second label compounds to the second plurality of beads inthe reactor. The first portion of the mixture may include the secondplurality of beads coupled to the first subset of the plurality ofsecond label compounds. Process 1400 may also include removing, usingthe solution, a second subset of the plurality of second label compoundsfrom the first portion of the mixture to form the second mixture mayinclude the second plurality of beads. Process 1400 may includemeasuring an amount of the first subset of the plurality of second labelcompounds coupled to the second plurality of beads in the secondmixture.

Labels of the label compounds may have different colors. For example, 2,3, 4, or 5 different colors of fluorophores can be used as labels. Asanother example, labels including quantum dots may have 2 to 5, 5 to 10,10 to 15, or more than 15 different colors. Multiple colors can be usedfor each bead size.

Process 1400 may be repeated two or more times. Process 1400 may includeadditional implementations, such as any single implementation or anycombination of implementations described herein and/or in connectionwith one or more other processes described elsewhere herein.

Although FIG. 13 shows example blocks of process 1400, in someimplementations, process 1400 may include additional blocks, fewerblocks, different blocks, or differently arranged blocks than thosedepicted in FIG. 13 . Additionally, or alternatively, two or more of theblocks of process 1400 may be performed in parallel.

V. Example Systems

FIG. 14 shows a system 1500 for analyzing reaction kinetics. System 1500may perform all or part of process 1400. In embodiments, system 1500 mayinclude a microfluidic chip 1504. Microfluidic chip 1504 may include areactor 1508. Reactor 1508 may have a volume from 1 to 5 μL, 5 to 10 μL,10 to 15 μL, 15 to 20 μL, 20 to 30 μL, or greater than 30 μL. Reactor1508 may have a volume of 20 μL or less. Reactor 1508 may be reactor404, reactor 816, or any reactor described herein. Reactor 1508 mayinclude an agitator (e.g., a stirrer) or a heater.

Microfluidic chip 1504 may include a structure array 1512. The structurearray may be a DLD array (e.g., DLD array 512). The structure array mayinclude a plurality of parallel rows of structures and a plurality ofparallel columns of structures. Microfluidic chip 1504 may have a firstlongitudinal axis 1540. The array of structures may have a secondlongitudinal axis 1544. Second longitudinal axis 1544 may be offset fromfirst longitudinal axis 1540. The axes may not be parallel. Secondlongitudinal axis 1544 and first longitudinal axis 1540 may form anangle from 10 to 20 degrees, 20 to 30 degrees, 30 to 40 degrees, 40 to50 degrees, 50 to 60 degrees, 60 to 70 degrees, or 70 to 80 degrees. Theangle formed may be an angle calculated with FIGS. 7A to 7C. Forexample, the angle may be equal to or within 5% or 10% of tan⁻¹ (1/N),where N is an integer from 1 to 30.

Each structure of the plurality of structures may be characterized by adiameter in a range from 1 to 2 μm, 2 to 3 μm, 3 to 4 μm, 4 to 5 μm, 5to 6 μm, 6 to 7 μm, 7 to 8 μm, 8 to 9 μm, 9 to 10 μm, 10 to 11 μm, 11 to15 μm, 15 to 20 μm, 20 to 30 μm, or greater than 30 μm. The structuresmay have a height from 1 to 2 μm, 2 to 3 μm, 3 to 4 μm, 4 to 5 μm, 5 to6 μm, 6 to 7 μm, 7 to 8 μm, 8 to 9 μm, 9 to 10 μm, 10 to 11 μm, 11 to 15μm, 15 to 20 μm, 20 to 30 μm, or greater than 30 μm. A structure may beseparate from the closest structure by a distance in a range from 1 to 2μm, 2 to 3 μm, 3 to 4 μm, 4 to 5 μm, 5 to 6 μm, 6 to 7 μm, 7 to 8 μm, 8to 9 μm, 9 to 10 μm, 10 to 11 μm, 11 to 15 μm, 15 to 20 μm, 20 to 30 μm,or greater than 30 μm. The height of the structures may be equal orabout equal (e.g., within 5%, 10%, or 20%) of the distance separating astructure from the closest structure. The diameter of the pillars may beequal or about equal to the height of the structures. The diameter ofthe beads may be calculated by the equation

${\frac{D_{C}}{G} \cong {\alpha \times \epsilon^{\beta}}},$as explained above. The diameter of the beads may be a function of thedistance between adjacent structures and the number of structures for ashift on structure to the right.

The structures may not be or include electrodes connected to a powersource or magnets. In embodiments, microfluidic chip 1504 may also notinclude electrodes or magnets.

Structure array 1512 may include a plurality of structures defining afirst fluidic path, which may be parallel or substantially parallel tosecond longitudinal axis 1544. The first fluidic path may be path 516 inFIG. 5A. The first fluidic path may be in fluid communication withreactor 1508, a solution reservoir 1516, and a manifold 1520 configuredto deliver a solution from solution reservoir 1516 to intersect thefirst fluidic path. The solution may be a buffer solution to clean thebeads. Solution reservoir 1516 may be buffer reservoir 820. The manifoldmay deliver the solution in a direction parallel to first longitudinalaxis 1540. For example, the path of the solution may be path 524 in FIG.5A.

In some embodiments, the plurality of structures may include differentsections of structures. In embodiments, each section of the structuresmay have a different longitudinal axis than an adjacent section. In someembodiments, each section of the structures may have different gapdistances, diameters, and/or heights than an adjacent section.

System 1500 may in addition include a plurality of beads disposed onmicrofluidic chip 1504. The plurality of beads may be disposed in supply1524. Supply 1524 may be a holding area for beads, analytes, and/orlabel compounds before they are introduced into reactor 1508. Each beadof the plurality of beads may have a diameter smaller than a width ofthe first fluidic path. Each bead of the plurality of beads may be boundto a first affinity reagent. The beads may be any beads describedherein, including bead 408, bead 550, bead 566, bead 604, bead 804, bead808, or bead 812. The first affinity reagent may be an antibody or anoligonucleotide. For example, the first affinity reagent may be antibody410 or any antibody described herein.

System 1500 may include a plurality of label compounds. The labelcompounds may not be coupled to the plurality of beads. Each labelcompound may include a second affinity reagent. Each second affinityreagent may be bound to a label. The second affinity reagent may be theantibody portion of labeled sandwich antibody 416. The second affinityreagent may be any antibody described herein. The label may be afluorophore, quantum dot, chemiluminescent tag, electrochemical tag, orany label described herein.

System 1500 may include a plurality of analytes. The analytes may be anyantigen described herein, including a protein. The plurality of firstaffinity reagents may be configured to bid to the analytes. Theplurality of second affinity reagents may be configured to bind to theplurality of analytes.

The analytes, affinity reagents, label compounds, and/or beads may belocated in supply 1524 or reactor 1508.

System 1500 may also include a detector 1528. Detector 1528 may be animaging detector (e.g., a camera). Detector 1528 may be positioned todetect and/or measure a signal in measurement area 1532. Measurementarea 1532 may be a portion of structure array 1512. Detector 1528 may beconfigured to detect the label. In some embodiments, detector 1528 maybe part of or contacting microfluidic chip 1504. Detector 1528 may becontrolled by computer system 1536. Computer system 1536 may receivedata from detector 1528. Data may indicate the intensity of the signaland/or a time when the signal was measured.

VI. Computer System

Any of the computer systems mentioned herein may utilize any suitablenumber of subsystems. Examples of such subsystems are shown in FIG. 15in computer system 10. In some embodiments, a computer system includes asingle computer apparatus, where the subsystems can be the components ofthe computer apparatus. In other embodiments, a computer system caninclude multiple computer apparatuses, each being a subsystem, withinternal components. A computer system can include desktop and laptopcomputers, tablets, mobile phones and other mobile devices.

The subsystems shown in FIG. 15 are interconnected via a system bus 75.Additional subsystems such as a printer 74, keyboard 78, storagedevice(s) 79, monitor 76 (e.g., a display screen, such as an LED), whichis coupled to display adapter 82, and others are shown. Peripherals andinput/output (I/O) devices, which couple to I/O controller 71, can beconnected to the computer system by any number of means known in the artsuch as input/output (I/O) port 77 (e.g., USB, Lightning). For example,I/O port 77 or external interface 81 (e.g. Ethernet, Wi-Fi, etc.) can beused to connect computer system 10 to a wide area network such as theInternet, a mouse input device, or a scanner. The interconnection viasystem bus 75 allows the central processor 73 to communicate with eachsubsystem and to control the execution of a plurality of instructionsfrom system memory 72 or the storage device(s) 79 (e.g., a fixed disk,such as a hard drive, or optical disk), as well as the exchange ofinformation between subsystems. The system memory 72 and/or the storagedevice(s) 79 may embody a computer readable medium. Another subsystem isa data collection device 85, such as a camera, microphone,accelerometer, and the like. Any of the data mentioned herein can beoutput from one component to another component and can be output to theuser.

A computer system can include a plurality of the same components orsubsystems, e.g., connected together by external interface 81, by aninternal interface, or via removable storage devices that can beconnected and removed from one component to another component. In someembodiments, computer systems, subsystem, or apparatuses can communicateover a network. In such instances, one computer can be considered aclient and another computer a server, where each can be part of a samecomputer system. A client and a server can each include multiplesystems, subsystems, or components.

Aspects of embodiments can be implemented in the form of control logicusing hardware circuitry (e.g. an application specific integratedcircuit or field programmable gate array) and/or using computer softwarewith a generally programmable processor in a modular or integratedmanner. As used herein, a processor can include a single-core processor,multi-core processor on a same integrated chip, or multiple processingunits on a single circuit board or networked, as well as dedicatedhardware. Based on the disclosure and teachings provided herein, aperson of ordinary skill in the art will know and appreciate other waysand/or methods to implement embodiments of the present disclosure usinghardware and a combination of hardware and software.

Any of the software components or functions described in thisapplication may be implemented as software code to be executed by aprocessor using any suitable computer language such as, for example,Java, C, C++, C#, Objective-C, Swift, or scripting language such as Perlor Python using, for example, conventional or object-orientedtechniques. The software code may be stored as a series of instructionsor commands on a computer readable medium for storage and/ortransmission. A suitable non-transitory computer readable medium caninclude random access memory (RAM), a read only memory (ROM), a magneticmedium such as a hard-drive, or an optical medium such as a compact disk(CD) or DVD (digital versatile disk) or Blu-ray disk, flash memory, andthe like. The computer readable medium may be any combination of suchstorage or transmission devices.

Such programs may also be encoded and transmitted using carrier signalsadapted for transmission via wired, optical, and/or wireless networksconforming to a variety of protocols, including the Internet. As such, acomputer readable medium may be created using a data signal encoded withsuch programs. Computer readable media encoded with the program code maybe packaged with a compatible device or provided separately from otherdevices (e.g., via Internet download). Any such computer readable mediummay reside on or within a single computer product (e.g., a hard drive, aCD, or an entire computer system), and may be present on or withindifferent computer products within a system or network. A computersystem may include a monitor, printer, or other suitable display forproviding any of the results mentioned herein to a user.

Any of the methods described herein may be totally or partiallyperformed with a computer system including one or more processors, whichcan be configured to perform the steps. Thus, embodiments can bedirected to computer systems configured to perform the steps of any ofthe methods described herein, potentially with different componentsperforming a respective step or a respective group of steps. Althoughpresented as numbered steps, steps of methods herein can be performed ata same time or at different times or in a different order that islogically possible. Additionally, portions of these steps may be usedwith portions of other steps from other methods. Also, all or portionsof a step may be optional. Additionally, any of the steps of any of themethods can be performed with modules, units, circuits, or other meansof a system for performing these steps.

As will be apparent to those of skill in the art upon reading thisdisclosure, each of the individual embodiments described and illustratedherein has discrete components and features which may be readilyseparated from or combined with the features of any of the other severalembodiments without departing from the scope or spirit of the presentdisclosure.

The above description of example embodiments of the present disclosurehas been presented for the purposes of illustration and description andare set forth so as to provide those of ordinary skill in the art with acomplete disclosure and description of how to make and use embodimentsof the present disclosure. It is not intended to be exhaustive or tolimit the disclosure to the precise form described nor are they intendedto represent that the experiments are all or the only experimentsperformed. Although the disclosure has been described in some detail byway of illustration and example for purposes of clarity ofunderstanding, it is readily apparent to those of ordinary skill in theart in light of the teachings of this disclosure that certain changesand modifications may be made thereto without departing from the spiritor scope of the appended claims.

Accordingly, the preceding merely illustrates the principles of theinvention. It will be appreciated that those skilled in the art will beable to devise various arrangements which, although not explicitlydescribed or shown herein, embody the principles of the invention andare included within its spirit and scope. Furthermore, all examples andconditional language recited herein are principally intended to aid thereader in understanding the principles of the disclosure being withoutlimitation to such specifically recited examples and conditions.Moreover, all statements herein reciting principles, aspects, andembodiments of the invention as well as specific examples thereof, areintended to encompass both structural and functional equivalentsthereof. Additionally, it is intended that such equivalents include bothcurrently known equivalents and equivalents developed in the future,i.e., any elements developed that perform the same function, regardlessof structure. The scope of the present invention, therefore, is notintended to be limited to the exemplary embodiments shown and describedherein. Rather, the scope and spirit of present invention is embodied bythe appended claims.

A recitation of “a”, “an” or “the” is intended to mean “one or more”unless specifically indicated to the contrary. The use of “or” isintended to mean an “inclusive or,” and not an “exclusive or” unlessspecifically indicated to the contrary. Reference to a “first” componentdoes not necessarily require that a second component be provided.Moreover, reference to a “first” or a “second” component does not limitthe referenced component to a particular location unless expresslystated. The term “based on” is intended to mean “based at least in parton.”

The claims may be drafted to exclude any element which may be optional.As such, this statement is intended to serve as antecedent basis for useof such exclusive terminology as “solely”, “only”, and the like inconnection with the recitation of claim elements, or the use of a“negative” limitation.

Where a range of values is provided, it is understood that eachintervening value, to the tenth of the unit of the lower limit unlessthe context clearly dictates otherwise, between the upper and lowerlimits of that range is also specifically disclosed. Each smaller rangebetween any stated value or intervening value in a stated range and anyother stated or intervening value in that stated range is encompassedwithin embodiments of the present disclosure. The upper and lower limitsof these smaller ranges may independently be included or excluded in therange, and each range where either, neither, or both limits are includedin the smaller ranges is also encompassed within the present disclosure,subject to any specifically excluded limit in the stated range. Wherethe stated range includes one or both of the limits, ranges excludingeither or both of those included limits are also included in the presentdisclosure.

All patents, patent applications, publications, and descriptionsmentioned herein are hereby incorporated by reference in their entiretyfor all purposes as if each individual publication or patent werespecifically and individually indicated to be incorporated by referenceand are incorporated herein by reference to disclose and describe themethods and/or materials in connection with which the publications arecited. None is admitted to be prior art.

What is claimed is:
 1. A method for analyzing reaction kinetics of abinding reaction, the method comprising: mixing a first plurality ofbeads with a sample to form a mixture in a reactor of a microfluidicchip, wherein: the sample comprises a plurality of analytes and aplurality of label compounds, each bead of the first plurality of beadsis coupled to an affinity reagent, the affinity reagent is configured tobind to the analyte, and the plurality of label compounds is configuredto bind to the analyte; binding the plurality of analytes to a pluralityof affinity reagents coupled to the first plurality of beads in thereactor; coupling a first subset of the plurality of label compounds tothe first plurality of beads in the reactor; flowing a first portion ofthe mixture from the reactor through a first fluidic path defined by aplurality of structures in the microfluidic chip, wherein: the firstportion of the mixture comprises the first plurality of beads coupled tothe first subset of the plurality of label compounds, the plurality ofstructures comprises a plurality of pillars, the plurality of pillars isa portion of an array of pillars, the array of pillars is characterizedby a plurality of rows and a plurality of columns, and the plurality ofpillars comprises pillars from at least five columns from the pluralityof columns; forming a second mixture comprising the first plurality ofbeads by flowing a solution in a second fluidic path, wherein the secondfluidic path intersects the first fluidic path; measuring an amount ofthe first subset of the plurality of label compounds in the secondmixture, wherein the second mixture is on the microfluidic chip duringthe measuring; and determining a reaction kinetic parameter using theamount of the first subset of the plurality of label compounds.
 2. Themethod of claim 1, further comprising: removing, using the solution, asecond subset of the plurality of label compounds from the first portionof the mixture to form the second mixture comprising the first pluralityof beads, wherein the second subset of the plurality of label compoundsis not coupled to the first plurality of beads.
 3. The method of claim1, wherein coupling the first subset of the plurality of label compoundsto the plurality of analytes occurs before binding the plurality ofanalytes to the plurality of affinity reagents.
 4. The method of claim1, wherein: the analyte is an antigen, the affinity reagent is anantibody, and each label of the plurality of label compounds comprises afluorescent label.
 5. The method of claim 1, wherein: the microfluidicchip has a longitudinal axis, and the first fluidic path and thelongitudinal axis form an angle in a range from 10 degrees to 60degrees.
 6. The method of claim 1, wherein: the microfluidic chip has alongitudinal axis, and the second fluidic path is parallel to thelongitudinal axis.
 7. The method of claim 1, wherein: the plurality ofanalytes is a first plurality of analytes, the method furthercomprising: removing, using the solution, a second plurality ofanalytes, wherein the second plurality of analytes is not coupled to thefirst plurality of beads.
 8. The method of claim 1, wherein measuringthe amount of label compounds comprises measuring a fluorescenceintensity.
 9. The method of claim 1, wherein the reaction kineticparameter is a concentration of the plurality of analytes.
 10. Themethod of claim 9, wherein determining the reaction kinetic parameterscomprises determining the concentration of the plurality of analytes isin a range from 1 pM to 500 pM.
 11. The method of claim 1, wherein thereaction kinetic parameter is a rate constant characterizing a bindingreaction of the affinity reagent to the analyte.
 12. The method of claim1, wherein: the plurality of analytes is a plurality of first analytes,the sample comprises a plurality of second analytes, the first analyteis different from the second analyte, and the plurality of affinityreagents is a plurality of first affinity reagents, the method furthercomprising: mixing a second plurality of beads with the sample to formthe mixture, wherein: each bead of the second plurality of beads iscoupled to a second affinity reagent, and the second affinity reagent isconfigured to bind to the second analyte, and binding the plurality ofsecond analytes to a plurality of second affinity reagents coupled tothe second plurality of beads.
 13. The method of claim 12, wherein: thefirst plurality of beads is characterized by diameters in a first sizerange, the second plurality of beads is characterized by diameters in asecond size range, and the first size range is not the second sizerange.
 14. The method of claim 13, wherein: the plurality of structuresis a first plurality of structures, the method further comprising:flowing a second portion of the mixture from the reactor through a thirdfluidic path defined by a second plurality of structures in themicrofluidic chip, wherein the second plurality of structures comprisesdifferent structures than the first plurality of structures.
 15. Themethod of claim 14, further comprising: coupling a third subset of theplurality of label compounds to the second plurality of beads in thereactor, removing, using the solution, a fourth subset of the pluralityof label compounds from the second portion of the mixture to form afourth mixture comprising the second plurality of beads, and measuringan amount of the third subset of the plurality of label compounds in thefourth mixture.
 16. The method of claim 12, wherein: the plurality oflabel compounds is a plurality of first label compounds, the samplefurther comprises a plurality of second label compounds, the pluralityof second label compounds is configured to bind to the second analyte,and the plurality of second label compounds is different from theplurality of first label compounds, the method further comprising:coupling a first subset of the plurality of second label compounds tothe second plurality of beads in the reactor, wherein: the first portionof the mixture comprises the second plurality of beads coupled to thefirst subset of the plurality of second label compounds, removing, usingthe solution, a second subset of the plurality of second label compoundsfrom the first portion of the mixture to form the second mixturecomprising the second plurality of beads, measuring an amount of thefirst subset of the plurality of second label compounds coupled to thesecond plurality of beads in the second mixture.
 17. The method of claim1, wherein: the analyte is a nucleic acid molecule, and the affinityreagent is an oligonucleotide comprising a sequence of nucleotidescomplementary to a portion of the nucleic acid molecule.
 18. The methodof claim 1, wherein each label compound of the plurality of labelcompounds comprises a quantum dot.
 19. The method of claim 1, whereinthe mixture in the reactor has a volume from 1 to 30 μL.
 20. The methodof claim 1, wherein the analyte is troponin I.